engleski

On the number of D(4)-quintuples

We call the set of m positive distinct integers a D(4)-m-tuple if the prod- uct of any of its two elements increased by 4 is a perfect square. The folklore conjecture states that there exists no D(4)-quintuple. In this talk we will present how to improve the known bound on the number of D(4)-quintuples, illustrating the more efficient way of counting the number of m-tuples using divisor sums. More precisely, we prove that there are at most 7*10^36 D(4)-quintuples.

Diophantine m-tuples; quintuple

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